Ocr 2024
OXFORD CAMBRDGE
AND RSA 2024
[Type the document subtitle]
OCR 2024
2024
[Type the company address]
, Oxford Cambridge and RSA
Monday 24 June 2024 – Afternoon A
Level Further Mathematics B (MEI) Y436/01
Further Pure with Technology
Time allowed: 1 hour 45 minutes
You must have:
• the Printed Answer Booklet
• the Formulae Booklet for Further Mathematics B
QP
(MEI)
• a computer with appropriate software
• a scientific or graphical calculator
INSTRUCTIONS
• Use black ink. You can use an HB pencil, but only for graphs and diagrams.
• Write your answer to each question in the space provided in the Printed Answer Booklet. If
you need extra space use the lined pages at the end of the Printed Answer Booklet. The
question numbers must be clearly shown.
• Fill in the boxes on the front of the Printed Answer Booklet.
• Answer all the questions.
• Where appropriate, your answer should be supported with working. Marks might be given
for using a correct method, even if your answer is wrong.
• Give your final answers to a degree of accuracy that is appropriate to the context.
• Do not send this Question Paper for marking. Keep it in the centre or recycle it.
INFORMATION
• The total mark for this paper is 60.
• The marks for each question are shown in brackets [ ].
• This document has 8 pages.
ADVICE
• Read each question carefully before you start your answer.
,OCR is an exempt Charity
Turn over
, 2
1 A family of curves is given by the equation
x2 - x + a2 - a
(*)
x-1
where the parameter a is a real number.
(a) (i) On the axes in the Printed Answer Booklet, sketch the curve in each of these cases.
• a =-0.5
• a =-0.1
• a = 0.5 [3]
(ii) State one feature of the curve for the cases a =-0.5 and a =-0.1 that is not a feature
of the curve in the case a = 0.5. [1]
(iii) By using a slider for a, or otherwise, write down the non-zero value of a for which the
points on the curve (*) all lie on a straight line. [1]
(iv) Write down the equation of the vertical asymptote of the curve (*). [1]
a2 - a
The equation of the curve (*) can be written in the form y = x + A + , where A is a
constant. x-1
(v) Show that A = 0. [2]
(vi) Hence, or otherwise, find the value of
x2 - x + a2 - a m
limc -x . [2]
x "3 x-1
(vii) Explain the significance of the result in part (a)(vi) in terms of a feature of the curve (*).
[1]
(b) In this part of the question the value of the parameter a satisfies 0 1 a 1 1. For values of a
in this range the curve intersects the x-axis at points X and Y. The point Z has coordinates
(0, -1). These three points form a triangle XYZ.
(i) Determine, in terms of a, the area of the triangle XYZ. [4]
(ii) Find the maximum area of the triangle XYZ. [2]
© OCR 2024 Y436/01 Jun24
OXFORD CAMBRDGE
AND RSA 2024
[Type the document subtitle]
OCR 2024
2024
[Type the company address]
, Oxford Cambridge and RSA
Monday 24 June 2024 – Afternoon A
Level Further Mathematics B (MEI) Y436/01
Further Pure with Technology
Time allowed: 1 hour 45 minutes
You must have:
• the Printed Answer Booklet
• the Formulae Booklet for Further Mathematics B
QP
(MEI)
• a computer with appropriate software
• a scientific or graphical calculator
INSTRUCTIONS
• Use black ink. You can use an HB pencil, but only for graphs and diagrams.
• Write your answer to each question in the space provided in the Printed Answer Booklet. If
you need extra space use the lined pages at the end of the Printed Answer Booklet. The
question numbers must be clearly shown.
• Fill in the boxes on the front of the Printed Answer Booklet.
• Answer all the questions.
• Where appropriate, your answer should be supported with working. Marks might be given
for using a correct method, even if your answer is wrong.
• Give your final answers to a degree of accuracy that is appropriate to the context.
• Do not send this Question Paper for marking. Keep it in the centre or recycle it.
INFORMATION
• The total mark for this paper is 60.
• The marks for each question are shown in brackets [ ].
• This document has 8 pages.
ADVICE
• Read each question carefully before you start your answer.
,OCR is an exempt Charity
Turn over
, 2
1 A family of curves is given by the equation
x2 - x + a2 - a
(*)
x-1
where the parameter a is a real number.
(a) (i) On the axes in the Printed Answer Booklet, sketch the curve in each of these cases.
• a =-0.5
• a =-0.1
• a = 0.5 [3]
(ii) State one feature of the curve for the cases a =-0.5 and a =-0.1 that is not a feature
of the curve in the case a = 0.5. [1]
(iii) By using a slider for a, or otherwise, write down the non-zero value of a for which the
points on the curve (*) all lie on a straight line. [1]
(iv) Write down the equation of the vertical asymptote of the curve (*). [1]
a2 - a
The equation of the curve (*) can be written in the form y = x + A + , where A is a
constant. x-1
(v) Show that A = 0. [2]
(vi) Hence, or otherwise, find the value of
x2 - x + a2 - a m
limc -x . [2]
x "3 x-1
(vii) Explain the significance of the result in part (a)(vi) in terms of a feature of the curve (*).
[1]
(b) In this part of the question the value of the parameter a satisfies 0 1 a 1 1. For values of a
in this range the curve intersects the x-axis at points X and Y. The point Z has coordinates
(0, -1). These three points form a triangle XYZ.
(i) Determine, in terms of a, the area of the triangle XYZ. [4]
(ii) Find the maximum area of the triangle XYZ. [2]
© OCR 2024 Y436/01 Jun24
